Can someone show me why
(a - b) ^2 - (c + d)^2 = (a-b-c-d)(a-b+c+d)
Use the difference of two squares pattern:
$\displaystyle x^2 - y^2 = (x - y)(x + y)$
Substitute "a - b" for x and "c + d" for y:
$\displaystyle \begin{aligned}
(a - b)^2 - (c + d)^2 &= [(a - b) - (c + d)][(a - b) + (c + d)] \\
&= (a - b - c - d)(a - b + c + d)
\end{aligned}$